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Physical Review A

Interference fringes of m=0 spin states under the Majorana transition caused by rapid half-rotation of a magnetic field

Atsushi Takahashi, Atsuo Morinaga

Published Apr 29, 2010• 0 citations
Publisher

Abstract

The phase shift and visibility of fringes in the Ramsey atom interferometer composed of the $|F=1$,${m}_{F}=0\ensuremath{\rangle}$ and $|F=2$,${m}_{F}=0\ensuremath{\rangle}$ states were examined systematically for rapid half-rotation of the magnetic field. It was verified that the phase shifts by $\ensuremath{\pi}$ rad in the adiabatic regime, but it does not shift from the original one in the nonadiabatic regime. These results support Robbins and Berry's claim [J. M. Robbins and M. V. Berry, J. Phys. A 27, L435 (1994)]. The fact that the interference fringes disappear in the intermediate regime and reappear in the nonadiabatic regime can be explained by the Majorana transition caused by a rapid reverse of the magnetic field.

DOI
10.1103/physreva.81.042111

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The phase shift and visibility of fringes in the Ramsey atom interferometer composed of the ∣F=1|F=1∣F=1,mF=0\ensuremath⟩{m}_{F}=0\ensuremath{\rangle}mF​=0\ensuremath⟩ and ∣F=2|F=2∣F=2,mF=0\ensuremath⟩{m}_{F}=0\ensuremath{\rangle}mF​=0\ensuremath⟩ states were examined systematically for rapid half-rotation of the magnetic field. It was verified that the phase shifts by \ensuremathπ\ensuremath{\pi}\ensuremathπ rad in the adiabatic regime, but it does not shift from the original one in the nonadiabatic regime. These results support Robbins and Berry's claim [J. M. Robbins and M. V. Berry, J. Phys. A 27, L435 (1994)]. The fact that the interference fringes disappear in the intermediate regime and reappear in the nonadiabatic regime can be explained by the Majorana transition caused by a rapid reverse of the magnetic field.
The $\ensuremath{\pi}$-phase shift between ∣F=1,mF=0⟩|F=1,{m}_{F}=0⟩∣F=1,mF​=0⟩ and ∣F=2,mF=0⟩|F=2,{m}_{F}=0⟩∣F=2,mF​=0⟩ states for an adiabatic rotation of a magnetic field observed in Ramsey atom interferometry arises from the negative sign of the transition amplitude between the ∣1,0⟩|1,0⟩∣1,0⟩ and ∣2,0⟩|2,0⟩∣2,0⟩ states when the wave functions are rotated to the opposite direction. Using a two-photon Raman atom interferometer with a cold ensemble of sodium atoms, the phase shift for a half-rotation of the magnetic field was confirmed to be $\ensuremath{\pi}\text{ }\text{rad}$ with an uncertainty of 4%, and the phase shift for a noncyclic adiabatic rotation of the magnetic field was investigated.
Using a magnetic-field-insensitive two-photon transition, the phase shift of atomic interference fringes and the frequency shift of the resonance spectrum were examined for a noncyclic rotation of a magnetic field during the interrogation time of an atom interferometer. We observed a phase shift proportional to the rotation angle of the magnetic field when the initial state and the final state were subjected to interference. We confirmed that the phase shift is equivalent to the scalar Aharonov-Bohm phase due to the geometrical potential. On the other hand, we demonstrated that the noncyclic Berry phase defined by the geodesic gauge is measurable using a strategy that the magnetic field rapidly returns to the initial direction during the interrogation time of the atom interferometer.
A Ramsey interrogation scheme was used to measure the phase shift of laser-cooled 87Rb^{87}\mathrm{Rb}87Rb clock-transition pseudospins arising as a result of a reversal of a bias-magnetic field, i.e., $\mathbf{B}\ensuremath{\rightarrow}\ensuremath{-}\mathbf{B}$, during the interrogation. While no phase shift occurred when the reversal was sudden, the Ramsey fringes were shifted by a factor of $\ensuremath{\pi}$ when the reversal was adiabatic. We thus verified the prediction that the spin states ∣F,m=0⟩|F,m=0⟩∣F,m=0⟩ acquire a purely topological and parity-dependent phase factor of $(\ensuremath{-}1{)}^{F}$ as a result of $\mathbf{B}\ensuremath{\rightarrow}\ensuremath{-}\mathbf{B}$.
An atom interferometer, whose arms are in the different sublevels, was demonstrated using two ${\ensuremath{\sigma}}^{+}$- and two ${\ensuremath{\sigma}}^{\ensuremath{-}}$-polarized, copropagating, laser beams in a magnetic field. Using the interferometer, Ramsey fringes with a width of 50 kHz were observed as a function of Zeeman shift frequency. The visibility of the interference fringes of 0.046 was obtained at an excitation power of almost $\ensuremath{\pi}/2$ pulse area.
Matter-wave interferometers with spin quantum states are attractive in quantum manipulation and precision measurements. Here, five spatial interference patterns corresponding to the full spin states are observed in each run of the experiment, by the combination of the Majorana transition according to the exponential modulation of the magnetic field pulse decline curve and radio frequency coupling among multiple magnetic sub-states. Compared to the realization of two Majorana transitions, the interference fringe for the magnetic field insensitive state also has a higher contrast. After spatially overlapping the full magnetic sub-state interference patterns dozens of times in consecutive experimental measurements, clear fringes are still observed, indicating the great stability of the relative phases of different components. This indicates the potential to achieve an interferometer with multiple spin clocks.
Summary form only given. The field of atom interferometry is experiencing rapid progress. Atom interferometers have been used to determine topological phase shifts such as the Aharonov-Bohm or Aharonov-Casher effects. Both two beam and more recently multiple beam atom interferometers have been realized. We report on an investigation of the electric (or scalar) Aharonov-Bohm effect in a multiple beam Ramsey experiment. The topological phase shift leads to collapse and revival of the fringe pattern. In a first interaction region cesium atoms are optically pumped into a dark coherent superposition of the magnetic quantum numbers m/sub F/=-4, -2, 0, 2 and 4 of the 6S/sub 1/2/ (F=4) ground state. The coherent superposition is probed after a time T in a second interaction region. When the atoms are irradiated in between the Ramsey interactions by an additional linearly polarized light field 400 MHz blue detuned to the F=4/spl rarr/F'=4 transition of the cesium D1 line, the induced AC Stark shift increases quadratically with the magnetic quantum number. The laser field coupling to the induced atomic dipole moment causes-in the absence of any classical forces-an electric Aharonov-Bohm phase shift.